Parallel Transformers Calculator – IEEE, IEC

Parallel transformers are essential in power systems to increase capacity and reliability by sharing loads efficiently. Calculating their parameters accurately ensures optimal performance and system stability.

This article covers detailed IEEE and IEC standards for parallel transformer calculations, including formulas, tables, and real-world examples. Engineers and technicians will gain comprehensive insights into design and analysis.

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Calculate load sharing for two transformers rated 500 kVA and 750 kVA in parallel.
Determine circulating current between two 1000 kVA transformers with 5% and 6% impedance.
Find the maximum load capacity when paralleling three transformers of 300 kVA, 400 kVA, and 500 kVA.
Evaluate voltage regulation differences for two parallel transformers with different %Z values.

Common Values for Parallel Transformers – IEEE and IEC Standards

Parameter	Typical Range	Units	Notes
Transformer Ratings (S_r)	50 – 5000	kVA	Common distribution and power transformers
Per Unit Impedance (Z_pu)	0.01 – 0.12	p.u.	Depends on transformer size and design
Voltage Rating (V_r)	400 – 132000	Volts (V)	Low to high voltage transformers
Percentage Impedance (%Z)	3 – 10	%	Typical for power transformers
Voltage Regulation	0.5 – 5	%	Depends on load and transformer design
Power Factor (cos φ)	0.7 – 1.0	Unitless	Load dependent

Detailed Formulas for Parallel Transformers Calculation (IEEE & IEC)

When transformers operate in parallel, the load divides inversely proportional to their per unit impedances.

Load on Transformer 1 (S1) = Stotal × (Z2 / (Z1 + Z2))

Load on Transformer 2 (S2) = Stotal × (Z1 / (Z1 + Z2))

S_total: Total load connected to transformers (kVA)
Z₁, Z₂: Per unit impedances of Transformer 1 and 2 (p.u.)
S₁, S₂: Load shared by Transformer 1 and 2 (kVA)

2. Circulating Current Between Parallel Transformers

Circulating current arises due to differences in voltage regulation or impedance and can cause overheating.

Icirculating = (Vrated / Zeq) × ((Z1 – Z2) / (Z1 + Z2))

V_rated: Rated voltage of transformers (Volts)
Z₁, Z₂: Per unit impedances of Transformer 1 and 2 (p.u.)
Z_eq: Equivalent impedance of transformers in parallel (p.u.)
I_circulating: Circulating current (Amperes)

3. Equivalent Impedance of Parallel Transformers

The equivalent impedance is calculated by the parallel combination of individual transformer impedances.

Zeq = (Z1 × Z2) / (Z1 + Z2)

Z_eq: Equivalent per unit impedance (p.u.)
Z₁, Z₂: Per unit impedances of Transformer 1 and 2 (p.u.)

4. Maximum Load Capacity of Parallel Transformers

The total maximum load capacity is the sum of individual transformer ratings, adjusted for impedance and load sharing.

Smax = S1 + S2 (if impedances and voltage ratings are matched)

S_max: Maximum combined load capacity (kVA)
S₁, S₂: Individual transformer ratings (kVA)

5. Voltage Regulation Difference Check

Voltage regulation differences must be within limits to avoid circulating currents and uneven load sharing.

|VR1 – VR2| ≤ 0.5%

VR₁, VR₂: Voltage regulation percentages of Transformer 1 and 2 (%)
IEC and IEEE recommend voltage regulation difference not exceeding 0.5% for parallel operation.

Real-World Application Examples

Two transformers rated 500 kVA and 750 kVA operate in parallel. Their per unit impedances are 0.06 and 0.05 respectively. Calculate the load shared by each transformer when the total load is 900 kVA.

Given:

S₁ = 500 kVA, Z₁ = 0.06 p.u.
S₂ = 750 kVA, Z₂ = 0.05 p.u.
S_total = 900 kVA

Step 1: Calculate load on Transformer 1:

S1 = 900 × (0.05 / (0.06 + 0.05)) = 900 × (0.05 / 0.11) ≈ 409.09 kVA

Step 2: Calculate load on Transformer 2:

S2 = 900 × (0.06 / (0.06 + 0.05)) = 900 × (0.06 / 0.11) ≈ 490.91 kVA

Interpretation: Transformer 1 carries approximately 409 kVA, and Transformer 2 carries approximately 491 kVA, matching their impedance ratios.

Example 2: Circulating Current Calculation Between Two Transformers

Two transformers rated at 1000 kVA each are connected in parallel. Their per unit impedances are 0.05 and 0.06 respectively. The rated voltage is 11 kV. Calculate the circulating current.

Given:

S₁ = S₂ = 1000 kVA
Z₁ = 0.05 p.u., Z₂ = 0.06 p.u.
V_rated = 11,000 V

Step 1: Calculate equivalent impedance:

Zeq = (0.05 × 0.06) / (0.05 + 0.06) = 0.003 / 0.11 ≈ 0.02727 p.u.

Step 2: Calculate circulating current magnitude:

Icirculating = (Vrated / Zeq) × ((Z1 – Z2) / (Z1 + Z2))

First, convert per unit impedance to ohms base:

Base current I_base = S_base / (√3 × V_rated) = 1000,000 VA / (1.732 × 11,000 V) ≈ 52.48 A
Base impedance Z_base = V_rated² / S_base = (11,000)² / 1,000,000 = 121 Ω
Equivalent impedance in ohms: Z_eq × Z_base = 0.02727 × 121 ≈ 3.3 Ω

Calculate the fraction:

(Z1 – Z2) / (Z1 + Z2) = (0.05 – 0.06) / (0.05 + 0.06) = -0.01 / 0.11 = -0.0909

Calculate circulating current in amperes:

Icirculating = (11,000 / 3.3) × 0.0909 ≈ 3333.33 × 0.0909 ≈ 303 A

Interpretation: A circulating current of approximately 303 A flows between transformers, which is significant and may cause overheating.

Additional Technical Considerations for Parallel Transformers

Voltage Ratio Matching: Transformers must have identical voltage ratios to avoid circulating currents.
Impedance Matching: Per unit impedances should be closely matched (within ±10%) for balanced load sharing.
Phase Displacement: Transformers must have the same vector group to ensure phase alignment.
Tap Changer Settings: Tap positions should be identical to maintain voltage equality.
Temperature Rise: Circulating currents increase losses and temperature; proper cooling is essential.
Standards Compliance: IEEE C57.12.70 and IEC 60076 provide guidelines for parallel operation.